Approximate higher-form symmetries and dualities of massive p-forms in the holographic bulk

Abstract

We develop a holographic framework for continuous higher-form symmetries and their low-energy effective descriptions, based on bulk path integrals, holographic renormalisation and boundary-condition-changing deformations. We show how approximate higher-form symmetries associated with a defect current can be realised holographically through massive antisymmetric tensor fields, either via parametrically small bulk masses or strong deformations associated with Robin boundary conditions. We further study the consequences of massless and massive Hodge dualities in the bulk, deriving the corresponding dualities between boundary theories related by different quantisation choices. Our results provide a unified perspective on approximate symmetries, dualities and strong/weak-coupling relations in holographic theories based on massive $p$-forms. In the self-dual case of an exact symmetry of degree $(d-3)/2$, we derive generalised constraints on holographic current-current correlators in the presence of double-trace deformations.